The first church in Svappavaara was built during the winter of 1957–1958, funded by a local collection begun in the early 1950s, and consecrated by Bishop Ivar Hylander on 16 November 1958. A burial chapel had already existed nearby at the old ironworks cemetery, though sources differ on whether it dates from the early 1600s or the 1920s. Remarkably, the congregation decided in December 1968 to replace this church while still only ten years old. The old building was demolished in January 1969, and the present church was consecrated by Bishop Stig Hellsten on 14 December 1969.
The current church is a timber-framed building that combines the nave with a parish hall, kitchen, rooms for children's and youth activities, an archive, and other facilities, all arranged around a small internal courtyard. Inside, the nave is lined with untreated wood panelling beneath a high ceiling supported by visible glued laminated timber beams, giving the space a plain, warm character typical of mid-twentieth-century Swedish church design. The floor is covered in linoleum, and pews are arranged in two open blocks seating just over a hundred people. A folding wall beside the altar can be opened to connect the nave with the adjoining assembly hall, allowing the space to be enlarged for larger gatherings. The church was renovated in 1994.
The altarpiece, painted by Albert Falck, survived from the earlier, short-lived church and was carried over into the new building, forming a physical link between the two structures. It carries a biblical inscription drawn from Matthew's Gospel. A church bell, donated by the mining company LKAB, was consecrated in December 1970. The organ, built by Grönlunds Orgelbyggeri of Gammelstad, is a mechanical instrument and was the church's first organ, though the exact year of its construction is not recorded.